Preservice Teachers’ Reasoning About Relationships That Are and Are Not Proportional: A Knowledge-in-Pieces Account

Past studies have documented students’ and teachers’ persistent difficulties in determining whether 2 quantities covary in a direct proportion, especially when presented missing-value word problems. In the current study, we combine a mathematical analysis with a psychological perspective to offer a new explanation for such difficulties. The authors illustrate how the combination of mathematical analysis and psychological perspective may be applied to data using empirical examples drawn from interviews during which preservice middle-grades teachers reasoned with varying degrees of success about relationships presented in word problems that were and were not proportional.